G2 surface problem (ISDX)

[mgnt8]

When smooth is desired you can't
beat a curve with no internal knots which, in Pro/E, means a
conic or a degree three curve with four control vertices

Indeed interesting how your spline-built VSS results in G2 continuity, tho I can't help but wonder if it wouldn't be better just using those fillet boundaries for a style surface with curvature contraints. Maybe if I have some time I'll look into it. One question -what is the origin, if any, of your relation: sd11 = 3 * sd7^2 / sd8 / 2?

 

[jeff4136]

As it was given to me; the radius at the end of a Bezier curve can be
calculated
r = curve degree * a^2 / b
where (for a curve with CV's 0, 1, 2, ...)
a = the length of the control polygon segment cv0 -> cv1
b = the distance to cv2 measured perpendicular to cv0 -> cv1


That didn't quite work out but some fiddling indicated
r = 3 * a^2 / b / 2
to be true for a spline curve with four CV's* and
r = 2 * a^2 / b
is true for a conic arc with rho = .5 (weight cv1 = 1).


* Where b = 0; e.g. when three CV's (0, 1 & 2 or 3, 2 & 1 for the
four CV curve) are colinear, Curvature will be zero.

 

[Beone]

Perfect job Jeff!!! I have downloaded that file and watch all steps, but there are some steps I never tryed I will try to learn it. How long did you make it?

 

[jeff4136]

How long?
We don't talk about that.

Seriously; a long time (days) trying to figure it out.
I have a terrible sense of time but ~think~ I could
probably duplicate it for a similar shape in a couple
of hours, less if I accept the blends without undue
fussing with trim curves and surface quality. The
sweeps and setup are tedious and time consuming but
not really difficult.


For practical purposes your blend / style feature is
probably the way to go. Which, by the way, I'd like
to see the surfaces if you can post or email a neutral
export (unless you're using WF2).

 

[burre]

My contribution to this discussion:








This is as far as I can get since I don't have more time for this. Most surfaces are g2 but I did not manage all. A good practice.


One thing I realised when modelling this one is that if all tubes are of the same diameter you can not have g2 between head tube ande the other two (you can but it will not look good, correct me if I'm wrong) due to the (obvious) behaviour of a g2 curve. In the following picture the horizontal curve isg1 and the otherg2.

 

[james.lynch]

you can.. but just not comming off the horizon line..

 

[jeff4136]

> One thing I realised when modelling this


That's why trim boundaries are more critical for G2 or G2+
transitions. You must consider the tangent direction AND
curvature. It's quite noticable and identifiable when
blending analytics like the cylinder and plane but equally
important for any surfaces if a nice, simple blend is the
goal. Trim both curves (arc and line) back from the
intersection. Try about 15 degrees of arc and about 5
degrees for the line. Adjust the setback and / or
constraint weight until you get an acceptable rate of
transition. You'll come out of round by about .1 - .2
percent of circle radius (.001 - .002 for a R1 circle) for
what I consider to be a 'nice' (e.g. the min rad for blend
curve is almost 1 for an R1 circle) transition.

 

[Jacoolo]

> In the end, really nice tutorials
> about - how to use sweep tool


Well, thank you. Happy to share the observations and thoughts.
(If you want to try something interesting with VSS; map the <br style="font-weight: bold; text-decoration: underline;">curvature on a relatively simple surface edge then drive a <br style="font-weight: bold; text-decoration: underline;">curvature dimensioned spline with an Evalgraph feature. It can <br style="font-weight: bold; text-decoration: underline;">be parametrically linked using an Evaluate feature.)

Jeff, I was playing with that idea in mind, but come without any example, could introduce one?

thanks in advance

 

[jeff4136]

> could introduce one?


When we're once again able to post attachments I'll put an example file
in the Surfaces Behavior discussion.

 

[Jacoolo]

to be true for a spline curve with four CV's* and
r = 2 * a^2 / b
is true for a conic arc with rho = .5 (weight cv1 = 1).

What about different conditions - any Rho?

 

[jeff4136]

> What about different conditions - any Rho?


I'm stretching for this stuff, don't have a firm grasp on it so
take it with a grain of salt ...
A conic with rho <> .5 (CV weight <> 1) isn't a Bezier spline so
the equation isn't appropriate. I'm sure there are ways of
calculating the curvature for elliptical and hyperbolic curves
but there may not be algebraic solutions. I've not found anything
within my very limited mathematical comprension range, anyway.

 

[Jacoolo]

it seems there is only left to create a spline between two conic arcs to maintain curvature, write relations and bua la, should work

one more feature or one less...

 

[mcgowanp]

Hey folks, I like the way these guys produce their G2 surfaces!


[url]http://videos.howstuffworks.com/howstuffworks/4168-assembly- line-cannondale-bicycles-video.htm [/url]


Paddy

 

[jeff4136]

... what is the origin, if any, of your relation: sd11 = 3 * sd7^2 / sd8 / 2?

... as it was given to me ...

Stumbled across something better ...
[url]http://www.tsplines.com/resources/class_notes/Bezier_curves. pdf[/url]
... section 2.6. Works without my 'monkey with football' derived
"/2" hack for the degree 3 curve.
2008-03-09_162008_bezier_crvtr_calc_rels.txt.zip
is a validation.

 

[design-engine]

I administered a four day surfacing class that included g2 continuity at Cannondale in 2005

Edited by: design-engine